Question

A species of animal is discovered on an island. Suppose that the population size Pt of the species can be modeled by the following function, where time t is measured in years. =Pt600+18e−0.45t Find the initial population size of the species and the population size after 8 years. Round your answers to the nearest whole number as necessary.

Answer 1

we have the function

`P(t)=(600)/(1+8e^((-0.45t)))`

Part 1

Find out the initial population

Remember that

The initial value is for t=0

so

substitute in the given function

`\begin{gathered} P(t)=(600)/(1+8e^((-0.45*0))) \\ \\ P(t)=(600)/(1+8) \\ P(t)=67 \end{gathered}`

the initial population is 67 individuals

Part 2

For t=8 years

substitute in the given function

`\begin{gathered} P(t)=(600)/(1+8e^((-0.45*8))) \\ P(t)=492 \end{gathered}`

The answer part 2 is 492 individuals